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Read more about APEX Calculus

APEX Calculus

Contributors: Hartman, Heinold, Siemers, Chalishajar, and Bowen

Publisher: APEX Calculus

This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 14. More information, including free downloads of .pdf versions of the text, is available at www.apexcalculus.com.

(5 reviews)

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Read more about Elementary Differential Equations with Boundary Value Problems

Elementary Differential Equations with Boundary Value Problems

Contributor: Trench

Publisher: A.T. Still University

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

(9 reviews)

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Read more about A Gentle Introduction to the Art of Mathematics

A Gentle Introduction to the Art of Mathematics

Contributor: Fields

Publisher: A.T. Still University

This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.

(2 reviews)

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Read more about Active Calculus 2.0

Active Calculus 2.0

Contributors: Boelkins, Austin, and Schlicker

Publisher: Grand Valley State University

Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.

(10 reviews)

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Read more about A Computational Introduction to Number Theory and Algebra

A Computational Introduction to Number Theory and Algebra

Contributor: Shoup

Publisher: Cambridge University Press

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.

(3 reviews)

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Read more about Linear Algebra

Linear Algebra

Contributors: Cherney, Denton, and Waldon

Publisher: University of California, Davis

We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book.

(2 reviews)

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Read more about Algorithms and Data Structures With Applications to Graphics and Geometry

Algorithms and Data Structures With Applications to Graphics and Geometry

Contributors: Nievergelt and Hinrichs

Publisher: Global Text Project

An introductory coverage of algorithms and data structures with application to graphics and geometry.

(1 review)

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Read more about Fundamentals of Mathematics

Fundamentals of Mathematics

Contributors: Burzynski and Ellis

Publisher: OpenStax CNX

Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who:

(8 reviews)

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Read more about Intermediate Algebra

Intermediate Algebra

Contributor: Redden

Publisher: Saylor Foundation

It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines.

(2 reviews)

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Read more about Calculus for the Life Sciences: A Modeling Approach Volume 2

Calculus for the Life Sciences: A Modeling Approach Volume 2

Contributors: Cornette and Ackerman

Publisher: James Cornette, Ralph Ackerman

Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course.

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